you're right that a mark next to an instance's name in an official list would look like Fluxer checked or vouches for that instance. so it won't be a badge or a check mark.
when the list is out, an instance run by someone with an Operator Pass gets a line of text in its listing instead, something like "The admin of this instance has an Operator Pass. Thank you for supporting Fluxer!" because the line says "Operator Pass" in full, it can't be confused with someone who just operates an instance.
every listed instance follows the same listing rules, and a pass never changes where an instance shows up on the list or how big its listing is. we also won't call it "donator", because the pass is a purchase, not a donation.
I've written this up in the help center and clarified this everywhere now: https://fluxer.com/help/operator-mark-on-instance-listings
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Comment by Hampus